Question 903490: Two cyclists leave towns 90mi apart at the same time and travel toward each other. One cyclist travels 8 /mih faster than the other. If they meet in 3 hours, what is the rate of each cyclist?
Found 5 solutions by richwmiller, Edwin McCravy, MathTherapy, ikleyn, greenestamps:
Answer by richwmiller(17219)   (Show Source):
Answer by Edwin McCravy(20077)  (Show Source):
You can put this solution on YOUR website!
What a grouch!
Two cyclists leave towns 90mi apart at the same time and travel toward each
other. One cyclist travels 8 mph faster than the other. If they meet in 3
hours, what is the rate of each cyclist?
rate • time = distance
slower cyclist x 3 3x
faster cyclist x+8 3 3(x+8)
The sum of their distances must equal the total distance they were
apart when they started.
3x + 3(x+8) = 90
3x + 3x + 24 = 90
6x + 24 = 90
8x = 66
x = 
The slower cyclist was going 8.25 mph and the faster one was going
8 mph faster or 16.25 mph.
Edwin
Answer by MathTherapy(10587)  (Show Source):
You can put this solution on YOUR website!
Two cyclists leave towns 90mi apart at the same time and travel toward each other. One cyclist travels 8 /mih
faster than the other. If they meet in 3 hours, what is the rate of each cyclist?
CORRECT ANSWERS: Slower cyclist's speed: 11 mph
Faster cyclist's speed: 11 + 8 = 19 mph
Answer by ikleyn(53427)  (Show Source):
You can put this solution on YOUR website! .
Two cyclists leave towns 90mi apart at the same time and travel toward each other.
One cyclist travels 8 miles per hour faster than the other.
If they meet in 3 hours, what is the rate of each cyclist?
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let x be the speed of the slower cyclist, in miles per hour.
Then the speed of the faster cyclist is (x+8) miles per hour.
The sum of their distances must equal the total distance they were
apart when they started.
3x + 3(x+8) = 90
3x + 3x + 24 = 90
6x + 24 = 90
6x = 66
x =  = 11 mph.
The slower cyclist was going 11 mph and the faster one was going
8 mph faster or 19 mph.
Solved correctly.
Answer by greenestamps(13258)  (Show Source):
You can put this solution on YOUR website!
While a solution using formal algebra is probably wanted, note that solving the problem informally, using logical reasoning and simple arithmetic instead of formal algebra, provides good mental exercise.
The two cyclists cover the total 90 miles in 3 hours, so their combined speed is 90/3 = 30 mph.
If they were cycling at the same speed, each of them would be going 30/2 = 15 mph.
Starting from that point in the reasoning, to make their speeds differ by 8 mph we need to increase one speed by 4 mph and decrease the other by 4 mph.
ANSWERS: 15+4 = 19 mph and 15-4 = 11 mph
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